Question

A triangle ABC can be constructed in which$\angle B={60}^o$, $\angle C={45}^o$ and AB +BC + AC = 11 cm. Is this Statement true?

• A. True
• B. False

Answer 1

The correct option is A True

$\because$ Sum of angles of a triangle=${180}^{\circ }$

$⟹\angle BAC=180-(60+45)={75}^{\circ }$

Now, to check the statement.

i)Draw a line segment XY=11cm.

ii)Make an angle equal to $\angle B=60$ from point X and mark L on this line.

iii)Make an angle equal to $\angle C={45}^{\circ }$ from point Y and mark M on this line.

iv)Bisect $\angle LXYand\angle MYX$,let the bisectors meet at point A.

v)Make perpendicular bisector of AX,let it intersect XY at B.

vi)Make perpendicular bisector of AY,let it intersect XY at point C.

vii)Join AB & AC ,Then measure AB+BC+AC.

If that is equal to 11cm.

The statement is true and ABC is the required triangle.